Upcoming Talks

Zahlentheoretisches Kolloquium

Title: Dirichlet Series with Periodic Coefficients and their Value-Distribution near the Critical Line
Speaker: Athanasios Sourmelidis (TU Graz)
Date: 17.7.2020, 13:30
Room: HS BE01, Steyrergasse 30
Abstract:

The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters.

We study the value-distribution of these Dirichlet series in a neighbourhood of the critical line (which is the abscissa of symmetry of the related Riemann-type functional equation).

In particular, for a fixed complex number $a\neq 0$, we consider for even or odd periodic $f$ the values taken at the $a$-points of the $\Delta$-factor of the functional equation, prove the existence of the mean-value of these points, show the uniform distribution of their ordinates, and obtain a related discrete universality theorem. This is joint work with Jörn Steuding and Ade Irma Suriajaya.

Remark: Athanasios Sourmelidis is a new member of the Institute of Analysis and Number Theory, where he will work as a PostDoc researcher.